A radioactive substance decays at a rate proportional to the amount present, and half the original quantity Qo is left after 1500 years. In how many years would the original amount be reduced to 3Q0/4? How much will be left after 2000 years?

Q: The half-life of strontium-90 is 28 years. How long will it take a 56 mg sample to decay to a mass…

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Q: If $6000 is invested at 3% compounded continuously, what is the amount after 8 years? The amount…

A: Answer  is   7625

Q: A certain radioactive material decays at a rate proportional to the amount present. At time ?=0,…

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Q: Of an initial amount of 6000 g of lead-210, how much will remain in 110 years? Lead-210 decays at a…

A:

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Given : S=the amount of radium you start with=250gm t=the amount of time in years=950 years  h=the…

Q: The radioactive isotope Carbon-14 has a half-life of 5,730 years. Given 300 grams of C-14, what is…

A: topic - exponential function

Q: The decay constant for the radioactive element strontium 90 is l = .0244, where time is measured in…

A: Definition used -                            Decay equation -…

Q: Radium decomposes at a rate proportional to the quantity present. If at the end of 20 years…

A: Solution

Q: How much should be invested at a rate of 7% coumpounded continuously to produce an amount of $15,000…

A:

Q: The half-life of Zn-71 is 2.4 minutes. If one had 135.0g at the beginning, how many grams would be…

A: We have to find

Q: of a radiooctive substonce decayed to 93.5% of its original sample amount after oyear What is the…

A: we need find half life substance k=? and t=?

Q: Of an initial amount of 5000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A:

Q: Of an initial amount of 9000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A: Apply the formula  P(t)=Po(1-r)t where, Po is the initial quantity r is the rate and t is the time.…

Q: There are 5,000 wolves in the park, but their population is expected to decay at a rate of 8% per…

A: Given, initially , wolves in the park = 5000 Decay of population = 8% per year finally , wolves in…

Q: Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100mg of radium…

A:

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A:

Q: Element X is a radioactive isotope such that every 70 years, its mass decreases by half. Given that…

A:

Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

A:

Q: if 8 g of a radioactive substance are present initially and 4 yr later only 4 g remain, how much of…

A:

Q: A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present…

A: It is given that,a radioactive substance has a decay rate of 4% per hour. If 1000 grams of the…

Q: Suppose you have 100g of Titanium-44, which has a half-life of 63 years. After how long will only 1g…

A: Initial amount=P=100  Half life= H= 63 years  Final amount= A= 1  Time= t years Using the half-life…

Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

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Q: How much money should be invested at a rate of 6% compounded continuously to produce an amount of…

A:

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 190 years? Lead-210 decays at a…

A: Here initial amount A0=4000g Decaying rate λ= 3.15% = 0.0315 Let amount remains in 190 years= A(t)

Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

A:

Q: Of an initial amount of 8000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A:

Q: A radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium…

A:

Q: A piece of machinery valued at $30,000 depreciates at a rate of 10% yearly. How long will it take…

A:

Q: Assume a substance has a half-life of 11 years and the initial amount is 133 grams.How long will it…

A: If A0 is initial amount present and T is half -life of the substance. Then the amount of substance…

Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 130 years? Lead-210 decays at a…

A: Find much much will remain

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A:

Q: 1. The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Since you posted two questions here, i can answer only first one at a time. Please repost other…

Q: Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000…

A: Given that the half life is 1000 years. This means 1/2 of the the original amount is left after 1000…

Q: An element with mass 640 grams decays by 7:3% per minute. How much of the element is remaining after…

A: Given intial mass =640 gmsRate of decay=7.3% per miniutetime =8 minute

Q: A 50 mg sample of thorium-233 decays to 44 mg after 4 min. a) Determine the half-life of…

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Q: A sample of radium has a weight of 1.5mg and a half-life of approximately 6 years how much of the…

A:

Q: If 12 g of a radioactive substance are present initially and 8 yr later only 6 g​ remain, how much…

A:

Q: If 16 g of a radioactive substance are present initially and 9 yr later only 8 g​ remain, how much…

A:

Q: A 50-mg sample of a radioactive substance decays to 34 mg after 30 days. How long will it take for…

A: The radioactive decay is modelled using the equation: N(t)=N0e-kt, where N0 is the initial amount…

Q: If 16 g of a radioactive substance are present initially and 5 yr later only 8 g​ remain, how much…

A:

Q: A tumor is injected with 0.7 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

A: The exponential function A = P * (1 - r)t  where A is the final amount and P is your inital amount.…

Q: Radium decomposes at a rate proportional to the amount present. If half of the original amount…

A:

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

Q: Element X is a radioactive isotope such that every 27 years, its mass decreases by half. Given that…

A: Radioactive decay

Q: Element X is a radioactive isotope such that every 28 years, its mass decreases by half. Given that…

A:

Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

Q: Element X decays radioactively with a half life of 8 minutes.If there are 980 grams of Element X,…

A: We have to find the time

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.